The temperature at a point (x, y, z) is given by T(x, y, z) = 300e-x² - 3y² - 9z² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, -1, 3) in the direction towards the point (6, -2, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P. Need Help? Read It
The temperature at a point (x, y, z) is given by T(x, y, z) = 300e-x² - 3y² - 9z² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, -1, 3) in the direction towards the point (6, -2, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P. Need Help? Read It
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.3: Rates Of Change
Problem 29E: Explain the difference between the average rate of change of y as x changes a to b, and the...
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![The temperature at a point (x, y, z) is given by
T(x, y, z) = 300e-x² - 3y2 - 9z²
where T is measured in °C and x, y, z in meters.
(a) Find the rate of change of temperature at the point P(2, -1, 3) in the direction towards the point (6, -2, 6).
°C/m
(b) In which direction does the temperature increase fastest at P?
73°F
Mostly cloudy
(c) Find the maximum rate of increase at P.
Need Help? Read It
Q
C
H
^ F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6147cd51-fae9-4b86-867f-e7a7fe5750a1%2F21c90b2f-b3bf-4d02-9074-e04871bf4007%2Fy7pdr2g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The temperature at a point (x, y, z) is given by
T(x, y, z) = 300e-x² - 3y2 - 9z²
where T is measured in °C and x, y, z in meters.
(a) Find the rate of change of temperature at the point P(2, -1, 3) in the direction towards the point (6, -2, 6).
°C/m
(b) In which direction does the temperature increase fastest at P?
73°F
Mostly cloudy
(c) Find the maximum rate of increase at P.
Need Help? Read It
Q
C
H
^ F
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